The approximation of expressions finds use in many fields of study and in diverse applications. For example, in Moving Picture Experts Group (MPEG) advanced audio coding (AAC) or layer 3 (MP3) audio decoders, a common process is inverse quantization. The AAC and the MP3 audio decoders perform an inverse non-uniform quantization for the spectral data after a Huffman decoding:xinq=sign(x)·|x|4/3 where xinq is the output of the inverse quantization and |x| is the input spectral data, ranging from 0 to 8191.
In one conventional system, a lookup table in the form of an 8k-word memory is employed such that, in this example, all 8192 possible values of |x| are matched with respective values of xinq. In many applications, an 8k-word memory takes up too much space in the chip.
On the other hand, in another conventional system, calculating xinq for each |x| in real (i.e., on the fly) by calculating the exponential function |x|4/3 requires an enormous amount of processing power.
Further limitations and disadvantages of conventional and traditional approaches will become apparent to one of ordinary skill in the art through comparison of such systems with the present invention as set forth in the remainder of the present application with reference to the drawings.